Ion transport in free and supported nitrobenzene aliquat nitrate liquid membrane ion-selective electrodes

Journal of Membrane Science, 4 (1979) 395-414 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

395

ION TRANSPORT IN FREE AND SUPPORTED NITROBENZENE ALIQUAT NITRATE LIQUID MEMBRANE ION-SELECTIVE ELECTRODES II. INTERFACIAL KINETICS AND TIME-DEPENDENT PHENOMENA

DALE E. MATHIS, FREDERICK

S. STOVER and RICHARD P. BUCK

William Rand Kenan Jr. Laboratories of Chemistry, Chapel Hill, North Curolina 27514 (U.S.A.)

The University of North Carolina,

(Received August 21,1978)

Summary Impedances for reversibly-contacted liquid ion exchanger membranes consisting of Aliquat nitrate dissolved in nitrobenzene were measured from 0.01 Hz to 0.5 MHz. Support-dependent impedances were observed as a second arc in the impedance plane diagrams. A slow rate for nitrate transport from aqueous solution to nitrobenzene was discovered and a kinetic rate constant for the reaction was estimated. Transient potential responses to ion steps from nitrate to chloride were studied empirically and simulated using a computer model. Non-monotonic potential responses showed good agreement with the model. The time course of hydration layer formation, at a supported liquid membrane, was studied by impedance methods and the effect of this layer on potentiometric time response was followed by measuring sequential concentration-step responses. Extensive hydration was found to occur in PVC-acrylonitrile supports, which suggested criteria for wettability by membrane solvent and for hydrophobicity for support materials.

Introduction Fundamental studies of ion transport in liquid ion exchange membranes are essential to the understanding and improvement of potentiometric sensors employing these membranes. Complete characterization of supported liquid systems cannot result solely from the elucidation of bulk membrane properties, such as ion pair formation, transport activation enthalpies, and dielectric properties. In addition, interfacial processes, such as slow ion transport kinetics and hydrated layer formation, must be understood if the potentiometric response of the resulting electrode is to be made predictable. In Part I of this series [l] the bulk properties of the Aliquat nitrate-nitrobenzene liquid ion exchanger were characterized by impedance measurements using blocking platinum contacts. In this .work the interfacial properties and some timedependent phenomena associated with these sensors have been studied by potentiometry and impedance measurements using reversible electrolyte contact The measurement geometry is identical to that employed for liquid membrane

396

electrodes and some results presented in this study represent properties of actual sensors. The water-nitrobenzene interface illustrates an ideal system for the study of ionic transport across phase boundaries. These solvents are immiscible and form a well-defined interfacial region. The high dielectric constant of nitrobenzene and the fact that it can be obtained in high purity [Z] combine to make it an excellent organic phase for studies of extraction, For these reasons, salt diffusion across a water-nitrobenzene phase boundary has been the subject of many scientific papers. An important early study of this type, done by Davies [3], reported forward and reverse salt transfer rates and thermodynamic activation parameters for several uniunivalent salts. Much more recently, however, the extensive work of Gavach et al. has dominated the study of interfacial phenomena in this system. Gavach has utilized chronopotentiometry and the measurement of b&ionic potentials to study ion transfer over-voltages [4-81 and salt distribution equilibria [g-11]. Their work includes the determination of ion transfer kinetic rate constants and transfer coefficients for several salts [12-141. An important feature of our work is that AC impedance measurements are successfully employed for the direct measurement of ion transfer kinetics. Gavach and Seta have used impedance measurements in the determination of double layer capacitance [15] and frequency-dependent impedance of the nitrobenzene-water interface with various depolarizers present [16]. Another relevent study by Brand and Rechnitz [17] involved impedance measurement on several commercial liquid membrane electrodes. While, in theory, these studies should be sensitive to interfacial rates of ion transport, the authors do not report rate constants and their impedance data do not show a clearly defined rate circle. This may be because measurements were not made at sufficiently high frequencies to detect interfacial processes or that large diffusional impedances obscured the charge transfer information. In this paper we employ AC impedance measurements to determine interfacial rates of ion transport at a water-nitrobenzene interface. The properties of artificial or support-generated impedances which appear as interfacial rates, are also investigated and a study of hydration layer formation has been undertaken using impedance measurements. Supporting potentiometric studies are included and computer simulation has been utilized to model empirically observed potential-time excursions which are hypothesized to be caused by temporal resolution of interfacial and diffusional potential developing processes. Experimental

Reagents Aliquat 3368 was obtained from General Mills and converted to the nitrate form by repeated equilibration with concentrated aqueous KN03. It was then washed with distilled deionized water and dried over molecular sieves. Reagent grade nitrobenzene used for this study was further purified by washing repeatedly

397

with aqueous 0.11w NazCOJ and then with distilled deionized water. The solvent was then vacuum distilled off of Linde 3A molecular sieves. Freshly distilled nitrobenzene prepared in this way has a specific conductance less than 0.02 micro-Siemen/cm. Polymer samples The following polymer support materials were obtained from Gelman; Metricel GA-8 (0.2 micron cellulose triacetate), Metricel Acropore AN450 (0.45 micron PVC-acrylonitrile copolymer), and Metricel#61757 (10.0 micron polypropylene). Instrumentation The admittance measuring instrument employed in this study is described in Part I [l]. The impedance cell used for reversible contact measurements on thick membranes (0.1-0.4 cm) was constructed in this lab and is displayed graphically in Fig. 1. Fig. 2 shows a cross-section of the assembled cell as it is used for a measurement. This cell design provides a well-defined membrane geometry essential for quantitative impedance measurements. The membrane area is 0.496 cm’. It is possible to obtain thicknesses from 0.1-0.4 cm in 1 mm steps. Polymer discs are used to constrain the bulk organic phase. SIX

FRONT

jt.5oc-j

--_--_-__-----~

-r 0

0

_-_-----*(y5 _ _ - - - - - - 0.rrng grmie _L

L!riii

7OP

8 4

__ ___ _____ _-_ .__ i10 B

C

_SN

SPACERS

Fig. 1. Graphic representation of parts for thick membrane reversible contact impedance cell. All dimensions are in inches.

398

Fig. 2. Cross-sectional view of assembled, thick-membrane, cell.

reversible-contact

impedance

Dialysis membrane with a molecular weight cut off of 6000-8000, obtained from Spectrum Medical Industries Inc., was found to effectively contain the liquid membrane without adding measurably to the cell impedance. Reversible contact measurements on thinner liquid membranes (less than 0.1 mm thickness) were made using the Orion series 92 liquid membrane electrode barrel and Ag/AgCl electrodes. An area of 0.023 cm* was measured for membranes mounted in this manner and the thickness is the same as that of the polymer support material used. Aqueous KNOB solutions saturated with AgCl and Ag/AgCl billets were used to achieve reversible contacts to the liquid membranes in all cases. Temperature was held at 25°C by immersing the cell in a thermostated oil bath as in Part I [l]. Procedure The “in phase” and “out of phase” admittances of reversibly-contacted, nitrobenzene-based liquid membranes were measured from 0.01 Hz to 560 kHz at quarter decade intervals. Membrane admittance was studied for several polymer supports and for thick and thin membranes. The time-dependent potentiometric response of thin membranes to concentration and ion steps was studied by the dip method [IS]. Calculations Real and quadrature impedances were calculated from the experimentally measured “in phase” and “out of phase” admittances and displayed as an impedance plane plot. Calculated quantities are all defined and determined from the data as specified in Part I [l].

399

Results and discussion I. Support-dependent

impedances

Frequency-dependent impedances, measured on 0.4 cm-thick AR Grade nitrobenzene membranes constrained by several support materials, are displayed in Fig, 3. Foreach support, the expected geometric or high frequency semicircle in the impedance plane plot is observed [19]. However, a second lower frequency semicircle can also be seen in two cases. This second arc is completely resolved for acrylic-coated polypropylene supports, but is very convoluted with the bulk arc for 10~ polypropylene. There are three recognized explanations for the low frequency arcs: a surface rate-controlled ion exchange, a surface film on or in the membrane support (analogous to the high resistance leach layer on glass electrodes), or an external or internal diffusion-controlled Warburg-like process [20]. From the transport parameters determined in Part I, external and internal diffusion control can be ruled out in the observed frequency range. If interfacial rates of ion transfer and internal diffusional behavior were controlling, the experimental method would show these features as three arcs [21], because the measurements were made using reversible contacts consisting of 0.1 M KNOJ saturated with AgCl and Ag/AgCl reference electrodes. The important observation that only the geometric arc is present when dialysis membrane supports are used suggests that slow interfacial, potential-dependent ion exchange is not the source of the

Z’

( Mn

-cm21

Fig. 3. Impedance plane diagram of 0.4 cm thick AR grade nitrobenzene liquid membrane as affected by constraining polymer. n, dialysis membrane; 0, 10~ polypropylene; l, acrylic coated polypropylene.

400

second semicircle. Rather, the second arc is caused by the high resistance of the support material as deduced from impedance analysis of supported and unsupported liquid ion exchange membranes. Membrane cells arranged in the manner of this measurement have properties of both free standing and supported ion exchanger and can exhibit a bulk arc for each. If the resistance and capacitance of the supported phase are sufficiently different from that of the free liquid, these arcs will be resolved in frequency even though the charge carriers are the same for both. This behavior is modeled as a series network of two parallel RC circuits and its theoretical behavior is depicted in Fig. 4 as a function of the difference in time constants for each circuit. Model values were chosen which gave the best comparison with the experimental data in Fig. 3 for 10~ polypropylene membrane supports. The impedance of the free standing liquid membrane is Z,(w) =LfR,/A(l

+ jwCgR_)

(1)

where w is the angular frequency, A the membrane area, L the membrane thickness, and R, and C, are the geometric resistivity and capacitance, respectively, of the free ion exchanger. The subscripts f and s designate properties of free standing and supported ion exchanger, respectively. When the support is an inert insulator, as is the case for polypropylene, the impedance of the supported phase can be written in terms of the polymer properties as follows: Z,(O) = L,R,

/F,A(l + jwCtR, )

(2)

Fig. 4. Model impedance plane diagram of a series network of two parallel RC circuits as a function of the ratio of their time constants.

401

where the quantity Fv represents been shown to equal [l] Ct = J’,C,

+ (I-

the void fraction

of the polymer

and Ct has (3)

F&&v

Since two supports impedance is

are utilized

to constrain

the free standing

liquid, the total

2+&t = Zf + 22, Z,,(w)

(4)

=(R,lA)[(&/(l

The resistance Rf = LfR,

+.&K&L)

+ 2L,/(J- +joCtR,)F,]

of each phase can be described

/A; R, = L,R,

by

/AF,

The quantity F, is, therefore, and is equal to

(5)

(6, 7)

experimentally

accessible

from this experiment (8)

FV = R&,/R& Using the data displayed in Fig. 3 in which two sheets of 10~ polypropylene 0.01 cm thick each are used to support a 0.4 cm thick membrane of free standing liquid ion exchanger, F, can be determined for this polymer as follows: F, = (0.23 Mfl-cm2,8X 0.02 cm)/(O.lO

Ma-cm’

X 0.40 cm) = 0.11

(9)

The experimental value of 0.11 determined by this method is in good agreement with the value of 0.10 + 0.01 determined in Part I [l] for this support, asserting the validity of this interpretation. It is, therefore, evident that a second arc can be generated in the impedance plane diagram by inhomogeneity in the bulk properties of a membrane along the axis of current flux. While this behavior has been demonstrated under somewhat contrived and artificial circumstances, it is very likely to appear in cases of inhomogeneous polymer degradation or curing as well. Coated wire sensors, for example, might well be subject to time constant distribution caused by this effect. It may be possible to use this artificial support-generated impedance to augment electrode selectivity coefficients if the resistance can be made to vary from ion to ion. II. Interfacial

ion transport kinetics Presented in Fig. 5 is a comparison of frequency-dependent impedances between a blocking-contact cell and a 0.4-cm-thick, reversible-contact cell containing 1 X 10e5 M Aliquat nitrate in nitrobenzene constrained with dialysis membrane. The blocking contact measurements (open circles) exhibit the expected low-frequency onset-of-blocking, capacitive behavior, whereas Warburg behavior is seen for the reversible contact measurement. Good agreement between high frequency or bulk resistances is observed. This behavior is expected when the ion exchange membrane is unaffected by exposure to aqueous solutions because high frequency resistance is independent of the type

402

.I

.2

.3 Z’

.4

.5

(MA-cm21

Fig. 5. Impedance plane diagram of 0.4 cm thick membrane of 1 x lo-’ M Aliquat nitrate in nitrobenzene. 0, platinum cell results; 0, reversible contact measurement with dialysis membrane constraint.

of interface used. This back-to-back comparison further substantiates the validity of earlier platinum cell measurements as applied to ion selective electrodes [l]. The DC resistance for the reversible contact measurement was calculated from transference number data in Part I as follows: R ,,c = R, (1 + t,/t_)

= 0.433 Ma-cm’(1

+ 0.25/0.75)

= 0.577 Ma-cm2

(10)

Very low frequency data points (less than 0.1 Hz) deviate from the calculated response, but have low reliability because of integrator drift and vibrational perturbations of the cell concentration profiles. For diffusional half-times of 10 s or more, convective stirring spoils profiles, as occurs in chronopotentiometric experiments at the same long times. Some unexplained impedance difference remains in Fig. 5 between the bulk and Warburg regions. Uncertainties are too large to assign an arc to these few points, or to invoke slow interfacial rates as the cause. To make impedance measurements more sensitive to interfacial rates, the membrane was reduced in thickness by using the Orion liquid membrane electrode barrel as the measurement cell. The interfacial impedance per unit area is unaffected by this change, but the bulk and diffusional impedances will be proportionally reduced. The reversible-contact impedance measurement for 0.01 cm-thick 8 X 10e4 M Aliquat nitrate, nitrobenzene-supported in PVC-acrylonitrile copolymer is shownin Fig. 6. Two arcs and a diffusional impedance can be assigned in the accessible frequency range. The observed high frequency impedance responsible for the non-zero intercept of the bulk properties arc

403

1.0

2.0 Z’

3.0

(Kn-cm2)

Fig. 6. Reversible contact impedance plane diagram of 0.01 cm thick membrane of 8 X 10e4 M Aliquat nitrate in purified nitrobenzene in a 0.45~ PVC-acrylonitrile copolymer membrane.

is attributed to the resistance of the 0.1 M KNOJ aqueous contacting solutions. This quantity, determined experimentally by blank measurements, can be taken as the intercept of the bulk arc for all of the ion exchanger runs. A bulk arc was then fit to this intercept and the high frequency data. A straight line intersecting the real axis was fit to low frequency diffusional data. The remaining impedance was then fitted for a single arc. It was not possible to use a least squares approach to fit all three processes simultaneously, since the bulk and interfacial arcs were lowered. The high frequency resistance for this system can be related to measurements made on a free standing liquid membrane as follows: Rf = R,F,/L,

= 1.44 KQ-cm’ X 0.36 * 0.04/0.0102

cm

(11)

The calculated value of 50.8 ? 5.0 KG-cm is in good agreement with the value of 45.2 KL2-cm measured for bulk nitrobenzene Aliquat solutions at the same concentration and temperature [l]. A second arc with a time constant of about 0.5 ms is observed, which is attributed to slow interfacial kinetics for transport of nitrate ion. Potentiometric studies of these membranes indicate that they are permeable only to anions, and since nitrate is the only anion present, interfacial rates must refer to nitrate. One can describe the ratelimiting reactions in a very general way as follows: No; (aq.)>NO;

(org.)

r

(12)

and define a charge transfer rate constant: ko = (lzfk,)‘”

(13)

The charge transfer resistance, RB , and the interfacial charge transfer rate

404

constant, kO, are related as follows: 2RT !2RT R, == F i” F2 kc, (c,,; CNo$‘*

(14)

For a surface rate constant to be apparent, the second semicircle must be at least 5% of the geometric R, or in this case k0 2 10q3 cm/s. Values computed from Fig. 6 give Iz, ~2.4 X 10m5 cm/s. The work of Davies [3] indicates that k0 for interfacial salt transport can vary from 10e4 to lo-’ cm/s for this system depending largely on the lipophilicity of the salt. Single ion transport is generally faster than salt transport and so k0 determined for nitrate in this study is in good agreement with these earlier measurements. The presence of slow interfacial nitrate ion transport kinetics in the nitrate ion selective electrode is an important discovery, and could play a significant role in controlling the membrane selectivity. It is already established that zero-current, steady-state bi-ionic systems can be kinetic-limited. This situation arises because steady-state systems are characterized by equal and opposite ionic fluxes, not zero flux as occdrs in membrane systems bathed in salts of a single permeant species. The effect was identified by Ciani et al. [22, 231. III. Transient responses to interferences A frequently observed, but previously unexplained, aspect of potentiometry at liquid ion exchange membranes is the non-monotonic potential-time response of these sensors to introduction of an interfering ion. If, for example, a nitrate ion selective electrode is removed from a sample solution of 0.01 M KNOB and stepped to 0.01 M KI, one observes a rapid negative excursion in potential which relaxes to a less negative value on a diffusional time scale of minutes [24]. No explanation of this behavior has appeared in the literature, but several empirical observations regarding the non-monotonic responses of calcium ion exchange membranes have been made [25]. The short time potential excursion has been shown to depend on stirring rate and not temperature, whereas the relaxation process does not depend on stirring rate but does depend on temperature. Additionally, we have observed that response to a step from the interferent back to the selective ion depends on the length of time the membrane has been in contact with the interferent solution, indicating that a compositional change is taking place in the membrane. Further, observation of non-montonic transient responses to interferences in the calcium liquid cation exchange electrode [25] implies that this phenomenon may be a property of liquid ion exchange membranes in general. Fig. 7 depicts the potential time response of a 2 X 10e3 M Aliquat nitratenitrobenzene membrane to ion steps from variable KNOJ concentrations to 1 M KCl. An important observation is that the transient is ur,affected in all cases by the KN03 concentration stepped from, and is controlled entirely by the KC1 concentration in solution. It should also be noted that the step from 10e4 M KN03 to 1 M KC1 is a monotonic transient. This information points

405

TIME

iseconds)

Fig. 7. Potentiometric response of 2 X lo-’ acetate membrane electrode to ion steps.

M Aliquat nitrate-nitrobenzene,

cellulose

to an explanation for ion step behavior which will be qualitatively presented here. The explanation proposed has been modeled by computer simulation and the results, which are presented and discussed in the Appendix, are in good agreement with the empirical data. When an ion selective membrane is removed from a bathing solution of the selective ion and placed in a solution of interferent, a rapidly developed interfacial potential is observed which is caused by the removal of surface concentration of the selective ion, nitrate in this case, and replacement by the interferent, chloride. This interfacial potential is established as rapidly as ion exchange kinetics or solution mass transport will allow. At longer times, the development of concentration profiles of the interfering ion and the coupled motion of sites result in a diffusion potential opposite in sign to the interfacial potential and appearing as a relaxation in the total potential. The steady state potential is then controlled both by the extractability and the mobility of the interfering ion. The explanation is presented more rigorously in the Appendix. Two conditions must be met to observe a non-monotonic transient: (1) interfacial relaxation must be significantly faster than diffusional relaxation so that the potential developing processes are resolved in time; and (2) the diffusion potential must be opposite in sign to the interfacial potential (as it is measured relative to the potential of the selective ion) so that an “overshoot” is observed. The first condition is almost always met unless the membrane exhibits very slow interfacial kinetics. The second condition is more constraining, but appears to be a common property of ion exchange

406

membranes for which the selectivity coefficients are controlled primarily by electrostatic considerations and not by specific solute-solvent or solute-ion exchanger interactions. Interfacial potentials are determined by ionic activity and extractability. For an electrostatic membrane (one employing an aprotic solvent), selectivity coefficients become larger with increasing ionic radius usually in the same order as the Hofmeister series. Diffusional potentials will, in the absence of non-uniform solvation effects, favor the smaller ion, once extracted, and generate a counter potential. Reinsfelder and Schultz [24] have, in fact, shown that a strong correlation exists between selectivity coefficients determined from peak potentials of non-monotonic transients and the extractability of the ion. This correlation does not hold as well for selectivity coefficients determined from steady state potentials since these values are strongly influenced by diffusional behavior as well. This result indicates that only immediately after the ion step is the potential controlled exclusively by interfacial concentrations. IV. Time-dependent phenomena Fig. 8 depicts the impedance plane diagram of the thin, reversible contact cell, studied in part II of the Results and discussion section, as a function of elapsed time. Closed circles are measured on a newly fabricated membrane and are essentially identical with the results in Fig. 6. Crosses and open circles represent impedances measured after 24 and 48 h, respectively. Measurements made at times longer than 48 h give the same result as those made at 48 h indicating the attainment of a steady state in that time. Both bulk and interfacial

c

2 E w I

5

1

=

N I

2

1

Z’

3

4

(Kn-cm21

Fig. 8. Reversible contact impedance plane diagram of the cell described in Fig. 6 as a function of time after fabrication. l, new; +, 24 h; 0, 48 h.

407

impedances are decreasing with elapsed time although time constants for these processes are fairly constant. This surprising fact indicates a geometric change in the membrane, rather than a change in activation parameters, because geometric changes cause resistance and capacitance to vary inversely and, therefore, do not affect time constants [26]. Changes in activation parameters would only affect the resistance associated with the activated transport process, and therefore would alter the time constant as well. Stated another way, the apparent changes in resistance with elapsed time occur because of variation of thickness or area, and not because of mobility changes. This result confirms the striking observation in Part I. Uptake of water by liquid membranes must be associated with changes (hydration) of the support, not with changes in the liquid phase or the transport properties of dissolved species. Potentiometric concentration-step studies of this membrane, on a comparable time scale, reveal several other important features associated with water uptake. The results of concentration step measurements from 10m2 to low3 M NO; are shown in Fig. 9. Curve a is the response of a new membrane; b was observed after 24 h and c after 48 h of exposure to bathing electrolyte. All measurements were done by the dip method at constant stirring. Results were normalized to $(t = -) - 4(t), to facilitate comparison in the presence of somewhat diminished response. An increase in the response time, which is indicative of formation of an increasingly thick stagnant film at the electrode surface [27--291, is observed with electrode “exposure” age. It should be noted that the conditioning effect described in Part I [l] of this series also takes place on this same time scale. A model involving formation of hydrated layers within the membrane support is schematically represented in Fig. 10, to account for these experimental observations. The rectangles in Fig. 10 represent an edge view of the polymer

lo-+$

0

12

24 TIME

36

48

KNO3

60

1

(seconds)

Fig. 9. Potentiometric response of 8 X 10m4M Aliquat nitrate-nitrobenzene, PVC-acrylonitrile membrane electrode to nitrate concentration step as a function of electrode age. a, new; b, 24 h; c, 48 h.

Time-Oh No Hydration

Fig. 10. Schematic = region m]

Tlme=24h Some Hydration

Tlme=48h Extensive Hydration

representation of hydration of membrane support with time. filled with ion exchanger; my = region hydrated.

support, and the rising cross hatch lines indicate the portion filled by the ion exchanger solution. Falling cross hatch lines are the hydrated portion of the support. These drawings illustrate the following observations: no hydration has occurred in a newly-fabricated membrane and the measured bulk impedance agrees with that predicted geometrically from the polymer thickness. The response to a concentration step is then most rapid, and is controlled entirely by an external, stirring-dependent stagnant film of solution. After 24 h of bathing external electrolyte exposure, some hydration has occurred and the actual liquid membrane thickness, and its associated resistance, have decreased. The time constant for bulk relaxation is, however, unchanged since the capacitance varies inversely with the membrane thickness, while the resistance has decreased linearly with thickness. Response to a concentration step is slower because of the longer time required for diffusion through the hydrated layer. Incidentally, the sensor will be electrically quieter or “conditioned” as described in Part I. The nitrobenzenewater interface is now inside the polymer support and, because of the fibrous nature of this material, the interface is more irregular, we believe. The resulting increase in interfacial surface area causes the apparent decrease in the interfacial impedance. Yet, the time constant remains unchanged because the double layer capacitance increases with interfacial area. Finally, at 48 h and steady state, hydration is extensive. All resistances are at their lowest values, and time responses are very long. The potentiometric response of the sensor is now somewhat reduced as well, probably because of the formation of small water channels all the way through the membrane. These channels compete with the membrane bulk for salt transport, but in a non-permselective manner, and therefore reduce the potential developed across the membrane. Under vigorous stirring the membrane will fail completely and irreversibly. If, however, prior to total failure, the electrode is taken out of water overnight, a return. to hydration conditions comparable to 24 h exposure is-observed. membrane

409

Conclusions

Application of impedance measurements to liquid membranes with reversible aqueous contacts has facilitated observation and explanation of several phenomena relevant to the use of these membranes as ion selective electrodes. These insights include: characterization of support-generated impedances, discovery of interfacial kinetics of nitrate ion transfer at a water-nitrobenzene interface, elucidation of the mechanism for non-monotonic potential responses to an ion step in mobile site membranes, and the time course and potentiometric effects of support hydration. The experimental conclusions of this work and their relevance to the response of ion selective electrodes are discussed here for each of these phenomena in the order listed above. A second arc observed in the impedance plane diagram of Aliquat nitratenitrobenzene membranes has been shown to be caused by inhomogeneity in the membrane composition along the axis of current flux. This arc is, in reality, a second bulk properties arc, and can be explained using the geometric resistance and capacitance of the ion exchanger-impregnated polymer support. A second arc is observed in this study only because both free standing and supported liquid ion exchanger exist simultaneously and in series under the measurement conditions employed, However, these results do indicate that a second arc can be observed whenever sufficient inhomogeneity exists as a function of membrane thickness. It has been shown that k0 = 2.4 X lo-’ cm/s for interfacial transport of nitrate ions across the water-nitrobenzene interface. The magnitude of this kinetic impedance is approximately equal to that of the bulk impedance for the ion exchanger concentrations and membrane dimensions used in typical ion selective electrodes. For this reason, the kinetic factors discovered here may significantly affect the properties of these sensors. In Part I it was demonstrated that the mobility of nitrate ion in the liquid membrane is unaffected by exposure to water and, therefore, that these ions are not hydrated in nitrobenzene. Davies’ study [3] confirms this observation and also demonstrates that stepwise exchange between water and nitrobenzene in the solvation sphere of the extracted ion is the rate-limiting process. In addition, it is shown that there is a linear free energy relationship between extraction kinetics and the partition ratio of a salt. Therefore, anions with larger extraction coefficients should be kinetically favored as well, and experimentally observed selectivity ratios should be greater than those predicted just from ionic extractability. This seems to be the case since selectivity coefficients measured for iron-phenanthroline nitrate/nitrobenzene liquid ion exchange membranes [24] are larger than values predicted from salt partition ratios. A model has been developed which accounts for the non-montonic potential response of a mobile site electrode to steps from the selective ion to an interference. This model requires that interfacial and diffusional potentials developed are opposite in sign and resolved in time. The essential conditions

410

for observation of a non-monotonic transient for ions i and j are: (1) I’f a$zi > ajkj then ui < Uj and the converse of this statement. (2) 7 interfacial < Tdiffusional(3) The confined site must be mobile. These conditions have been used in a computer simulation of the ion step experiments carried out in this study and both theoretical and empirical results are in good qualitative agreement. Finally, the time course of membrane hydration has been elucidated for PVC-acrylonitrile supports and hydration effects on the potentiometry and response time of the electrode have been demonstrated. Hydration was shown to increase response time to a concentration step as a result of slow diffusion through thick stagnant aqueous films. Extensive hydration resulted in a partial loss of Nernstian response for the sensor, probably because water channel formation through the membrane competes for salt transport in a non-permselective manner. A decrease of sensor noise levels was also observed on the same time scale and is attributed to the reduction of electrode impedance caused by hydration. These results indicate that the membrane solvent and aqueous solution compete to wet the support polymer and that a useful support must be hydrophobic and wettable by the membrane solvent as well as inert. Acknowledgements This work was supported by National Science Foundation Grant CHE-7500970-A01 and CHE77-20491. Symbols list A

a+, act CPOlY

2 f .0 1 j bv

kr

ko ki,

kj

L R

R, Rf,Rs R DC

active membrane area (cm”) activities of electrolyte solution species total system capacitance capacitance of membrane support geometric capacitance Faraday subscript for “free standing” exchange current density (amps/cm2) t/-l forward and backward rate constants (cm/s) standard rate constant (cm/s) single ion partition coefficients membrane thickness (cm) gas constant infinite frequency resistance of whole membrane and support (ohm-cm2) infinite frequency resistances of free standing membrane and support ( ohm-cm2) DC resistance (ohm-cm’)

411

43 s

T tot

t+, tUi9 Uj V

surface “activation” resistance (ohm-cm2) subscript for “support” absolute temperature subscript for “total” transference numbers of membrane ionic species single ion mobilities subscript for “void” angular frequency (radians/s) impedance function of jo

&J)

References 1 D.E. Mathis and R.P. Buck, J. Membrane Sci., 4 (1979) 379. 2 T. Iwachido, Bull. Chem. Sot. Japan, 44 (1971) 1835. 3 J.T. Davies, J. Phys. Chem., 54 (1950) 185. 4 C. Gavach and B.D’Epenoux, J. Electroanal. Chem., 55 (1974) 59. 5 C. Gavach and F. Henry, J. Electroanal. Chem., 54 (1974) 361. 6 C. Gavach, J. Chim. Phys. Physiochim. Biol., 70 (1973) 1478. 7 C. Gavach and F. Henry, C.R. Acad. Sci., Ser. C., 274 (1972) 1545. 8 C. Gavach, T. Mlodnicka and J. Gustalla, CR. Acad. Sci., Ser. C., 266 (1968) 1196. 9 C. Gavach and A. Savajols, Electrochim. Acta., 19 (1974) 575. 10 C. Gavach, Electrochim. Acta., 18 (1973) 649. 11 C. Gavach, CR. Acad. Sci., Ser. C., 266 (1969) 1356. 12 C. Gavach, B. D’Epenoux and F. Henry, J. Electroanal. Chem., 64 (1975) 107. 13 C. Gavach, F. Henry and R. Sandeaux, C.R. Acad. Sci., Ser. C., 278 (1974) 491. 14 C. Gavach and F. Henry, C.R. Acad. Sci., Ser. C., 274 (1972) 1549. 15 C. Gavach, P. Seta and F. Henry, Bioelectrochem. Bioenerg., 1 (1974) 329. 16 C. Gavach and P. Seta, C.R. Acad. Sci., Ser. C., 275 (1972) 1231. 17 M.J.D. Brand and G. Rechnitz, Anal. Chem., 41 (1969) 1135. 18 G. Rechnitz, Talanta, 11 (1964) 1467. 19 R.P. Buck, Crit. Rev. Anal. Chem., 5 (1975) 323. 20 R.P. Buck,,Anal. Chem., 48 (1976) 23R. 21 T. Brumleve and R.P. Buck, J. Electroanal. Chem., 90 (1978) 1. 22 S. Ciani, R. Laprade, G. Eisenman and G. Szabo, J. Membrane Biol., 11 (1973) 255. 23 G. Eisenman (Ed.), Membranes, Vol. 2, Marcel Dekker, New York, 1973, p. 61. 24 R. Reinsfelder and F. Schultz, Anal. Chim. Acta., 65 (1973) 425. 25 J. Bagg and R. Vinen, Anal. Chem., 44 (1972) 1773. 26 D.E. Mathis, R.K. Rhodes and R.P. Buck, J. Electroanal. Chem., 80 (1977) 245. 27 A. Shatkay, Anal. Chem., 48 (1976) 1039. 28 E. Lindner, K. Toth and E. Pungor, Anal. Chem., 48 (1976) 1071. 29 W.E. Morf, E. Lindner and W. Simon, Anal. Chem., 47 (1975) 1596. 30 S.W. Feldberg, in A.J. Bard, Ed., Electroanalytical Chemistry, Marcel Dekker, New York, Vol. 3, 1969, p. 200. 31 F.S. Stover and R.P. Buck, BiophysJ., 16 (1976) 753. 32 J.R. Sandifer and R.P. Buck, J. Phys. Chem., 79 (1975) 384. 33 F.S. Stover and R.P. Buck, J. Phys. Chem., 81 (1977) 2105.

412

Appendix. Simulation of ion-step time responses of liquid ion exchange membranes Digital simulation [30] is a successful technique for solving problems in membrane electrochemistry [Zl, 31-331. One of the most powerful applications is the investigation of time-dependent and frequency-dependent properties of membrane systems. In previous work 1311 we found varied potential-time responses to external activity changes for dissociated and ion-paired membranes. These could be placed into categories related to the well-known time constants for current-step perturbations. The simulation reported here attempts to elucidate the origin of non-monotonic potential changes after a change in the external electroactive species. Details of the simulation procedure can be found elsewhere [31,32]. The membrane system is an ideal, univalent, positively charged, mobile-site anion exchanger system. It has been assumed that the membrane is completely electroneutral, has unit internal activity coefficients, has distance independent mobilities, and obeys the dilute solution form of the Nernst-Planck flux equations. The perturbation of the system is a change from a pure solution of an old ion, O-, to a pure solution of a new ion, N-, at the same activity. The difference between the final, steady-state potential and the initial potential of this system can be expressed as #_

-cp,=-~l"(

a’N kN

uN

a'0 ko

uo 1

(Al)

where k is a single ion extraction coefficient, u is a mobility, a’ is an external test activity, @_ is the steady-state potential after the ion step, and Go is the steady-state potential prior to the ion step. From the logarithmic term in eqn. (Al), it can be seen that two ratios affect the steady-state potential value: the extraction ratio and the mobility ratio. These two ratios are expected to influence the potential response of liquid ion exchange membranes in two different time ranges. The extraction ratio., which governs the ion exchange reaction at the interfaces, is expected to dominate the interfacial potential difference established at short times. The mobility ratio, which governs transport of ions through the membrane and formation of internal diffusion potentials, is expected to influence the overall potential change at later times. If the logarithm of these two ratios are opposite in sign, a non-monotonic time response should result. Fig. 11 shows the potential-time response to an ion step with the above conditions met. The time scale is in reduced units which have been normalized by the membrane diffusion time. The values of the ratios are kN /k. = 0.25 and UN/uo = 2.0, and an overshoot is observed in the response. The initial potential change, governed qualitatively by the extraction ratio, is seen to be less than the predicted -ln(k, /k, ) = 1.39. The reason is that while extraction at the interface is occurring, electric fields build up just internal to the interface. These fields give rise to diffusion potentials which oppose the interfacial

413

0

100

1

200

I

300

400

500

600

I

700

800

900

time Fig. 11. Simulated UN/U0 = 2.0.

potential-time

response

to an ion step for which

h,/ko

= 0.25

and

potential (or reinforce it for the case where the logarithms of the two ratios are the same sign). The result is that one cannot completely time-resolve the interfacial and diffusional potentials to predict quantitatively the time course of the total potential. Also, non-steady-state potentials are affected by the mobility of the exchange site. The percent of the extraction ratio which corresponds to the initial interfacial potential difference varies in response to the site mobility. Simulations performed with varying site mobility show that, for high site mobilities, nearly all of the theoretical “pure” interfacial potential can be realized. For low site mobilities, a lower percentage can be seen [31], and, in the limit of a fixed-site membrane (zero site mobility) the steady state potential occurs immediately. The second transient shown in Fig. 11 is obtained by stepping back to the original external solution composition. The long time response is the negative of the first, as would be predicted from equation Al and the preceding discussion. For a given membrane composition, the magnitude and shape of the long time transient is independent of the actual values of C& and ab , as long as the step is from a mono-ionic to a bi-ionic case. A non-monotonic time response to an ion step of equal activities indicates inverse selectivity behavior of extraction coefficients and mobilities, i.e., 12, /k, > 1 and UN/u. < 1 or vice versa. When kN /k, and UN/u. are both greater than or less than 1, the initial interfacial potential difference and the diffusional contribution are the same sign. For that case, a monotonic transient is predicted.